Answer:
(a) ![\frac{7}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B8%7D)
(b) ![\frac{9}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B10%7D)
Step-by-step explanation:
Given,
P(A) = 0.5 ⇒ ![P(A^c)=1-P(A) = 1 - 0.5 = 0.5](https://tex.z-dn.net/?f=P%28A%5Ec%29%3D1-P%28A%29%20%3D%201%20-%200.5%20%3D%200.5)
P(B) = 0.6 ⇒ ![P(B^c)=1-P(B) = 1 - 0.6 = 0.4](https://tex.z-dn.net/?f=P%28B%5Ec%29%3D1-P%28B%29%20%3D%201%20-%200.6%20%3D%200.4)
P(A∩B) = 0.15
∵ ![P(A\cap B^c)=P(A) - P(A\cap B) = 0.5 - 0.15 = 0.35](https://tex.z-dn.net/?f=P%28A%5Ccap%20B%5Ec%29%3DP%28A%29%20-%20P%28A%5Ccap%20B%29%20%3D%200.5%20-%200.15%20%3D%200.35)
Similarly,
Now,
(a) ![P(\frac{A}{B^c})=\frac{P(A\cap B^c)}{P(B^c)}=\frac{0.35}{0.4}=\frac{35}{40}=\frac{7}{8}](https://tex.z-dn.net/?f=P%28%5Cfrac%7BA%7D%7BB%5Ec%7D%29%3D%5Cfrac%7BP%28A%5Ccap%20B%5Ec%29%7D%7BP%28B%5Ec%29%7D%3D%5Cfrac%7B0.35%7D%7B0.4%7D%3D%5Cfrac%7B35%7D%7B40%7D%3D%5Cfrac%7B7%7D%7B8%7D)
(b) ![P(\frac{B}{A^c})=\frac{P(B\cap A^c)}{P(A^c)}=\frac{0.45}{0.5}=\frac{45}{50}=\frac{9}{10}](https://tex.z-dn.net/?f=P%28%5Cfrac%7BB%7D%7BA%5Ec%7D%29%3D%5Cfrac%7BP%28B%5Ccap%20A%5Ec%29%7D%7BP%28A%5Ec%29%7D%3D%5Cfrac%7B0.45%7D%7B0.5%7D%3D%5Cfrac%7B45%7D%7B50%7D%3D%5Cfrac%7B9%7D%7B10%7D)
Answer:
y = -5
Step-by-step explanation:
To solve for a variable, take the following steps:
- Distribute by multiplying into each term in the parenthesis
- Combine like terms
- Move terms across the equal sign using inverse operations
2 - 4 (y + 4) = 2y + 16 Distribute
2 - 4y - 16 = 2y + 16 Combine 2-16
-14 - 4y = 2y + 16 Add 4y to both sides
-14 = 6y + 16 Subtract 16 to both sides
-30 = 6y Divide by 6
y = -5
3/9, 30/90, 45/135
all you have to do is divided the numerator and denominator by a common factor or multiply by the same number
It would happen again at 1 hour and 5 minutes .
That is because at noon it is 12 p.m. and for the minute and the hour hands overlap, the next time it would happen is at 1:05 which is going to overlap again
It should be true. As the number goes more right the number is getting bigger hence the name "greatest common divisor".